The economic organisation N-56 also calls on ministers to set up an investment bank dedicated to hydrocarbon to boost investment in an area seen as vital to future energy needs.
The SNP has said under independence its planned new energy ministry would be "co-headquartered" in Aberdeen and Glasgow.
For their part, Tory-Lib Dem ministers at Westminster pledged funding earlier this year to help the North Sea release its potential, as they visited Aberdeen for a cabinet meeting.
The recommendations are included in a new report, Oil and Gas - a Pivotal Moment, designed to make Scotland one of the top five wealthiest countries in the world.
The report also calls for a more competitive tax system. All recommendations should be implemented regardless of whether or not Scots vote for independence, the think tank says.
BiGGAR Economics' Graeme Blackett, from N-56, said: "With 90 per cent of the oil and gas reserves in Scottish waters, whether independent or not, it is vital that those policy and decision makers responsible for taxation and regulation of the sector are located in Aberdeen."
Responding to the report, Fergus Ewing, the Scottish Government energy minister, hailed it as an endorsement of the SNP's plans.
He said: "Successive Westminster Governments have failed to maximise the benefit from North Sea oil and gas resources."